Chapter 2: Q37E (page 94)
Explain how the relationship between the mean and median provides information about the symmetry or skewness of the data’s distribution.
If the mean is to the right, the distribution is skewed to the right.
If the mean is to the left, the distribution is skewed to the left.
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Is honey a cough remedy?Refer to the Archives of Pediatrics and Adolescent Medicine(Dec. 2007) studyof honey as a remedy for coughing, Exercise 2.31 (p. 86). Recall that the 105 ill children in the sample wererandomly divided into three groups: those who receiveda dosage of over-the-counter cough medicine (DM),those who received a dosage of honey (H), and thosewho received no dosage (control group). The coughingimprovement scores (as determined by the children’sparents) for the patients are reproduced in the nexttable.
Honey Dosage | 12, 11, 15, 11, 10, 13, 10, 4 ,15, 16, 9, 14, 10, 6, 10, 8, 11, 12, 12, 8, 12, 9, 11, 15, 10, 15, 9, 13, 8, 12, 10, 8, 9, 5, 12 |
DM Dosage | 4, 6, 9, 4, 7, 7, 7, 9, 12 ,10, 11, 6, 3, 4, 9, 12, 7, 6, 8, 12, 12, 4, 12, 13, 7, 10 |
No Dosage | 13, 9, 4, 4, 10, 15, 9, 5, 8, 6, 1, 0, 8, 12, 8, 7, 7, 1, 6, 7, 7, 12, 7, 9, 7, 9, 5, 11, 9, 5, 6, 8, 8, 6, 7, 10, 9, 4, 8, 7, 3, 1, 4, 3 |
a) Find the median improvement score for the honey dosage group.
b) Find the median improvement score for the DM dosage group.
c) Find the median improvement score for the control group.
d) Based on the results, parts a–c, what conclusions can pediatric researchers draw? (We show how to support these conclusions with a measure of reliability in subsequent chapters.)
STEM experiences for girls. The National Science Foundation (NSF) sponsored a study on girls’ participation in informal science, technology, engineering, or mathematics (STEM) programs. The results of the study were published in Cascading Influences: Long-Term Impacts of Informal STEM Experiences for Girls (March 2013). The researchers sampled 174 young women who recently participated in a STEM program. They used a pie chart to describe the geographic location (urban, suburban, or rural) of the STEM programs attended. Of the 174 STEM participants, 107 were in urban areas, 57 in suburban areas, and 10 in rural areas.
a. Determine the proportion of STEM participants from urban areas.
b. Determine the proportion of STEM participants from suburban areas.
c. Determine the proportion of STEM participants from rural areas.
d. Multiply each proportion in parts a—c by 360 to determine the pie slice size (in degrees) for each location.
e. Use the results, part d, to construct a pie chart for the geographic location of STEM participants.
f. Interpret the pie slice for urban areas.
g. Convert the pie chart into a bar graph. Which, in your opinion, is more informative?
Budget lapsing at army hospitals.Accountants use the term budget lapsingto describe the situation that occurs when unspent funds do not carry over from one budgeting period to the next. Due to budget lapsing, U.S. army hospitals tend to stockpile pharmaceuticals and other supplies toward the end of the fiscal year, leading to a spike in expenditures. This phenomenon was investigated in the Journal of Management Accounting Research(Vol. 19, 2007). Data on expenses per full-timeequivalent employees for a sample of 1,751 army hospitalsyielded the following summary statistics: xbar= \(6,563,m= \)6,232, s= \(2,484, QL = \)5,309 and QU = \(7,216.
a.Interpret, practically, the measures of relative standing.
b.Compute the interquartile range, IQR, for the data.
c.What proportion of the 1,751 army hospitals have expenses between \)5,309 and $7,216?
Construct a scattergram for the data in the following table.
Variable 1: 174 268 345 119 400 520 190 448 307 252 Variable 2: 8 10 15 7 22 31 15 20 11 9 |
Construct a relative frequency histogram for the data summarized in the accompanying table.
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